Unramified multiplet-frequency conjecture for totally real cubic fields

Let $K=\mathbb{Q}(\sqrt{d})$ be a quadratic field with $3$-class rank $\varrho$, and let the associated unramified nilets, singlets, and quartets be classified by their types. The percentages below refer successively to the upper bounds $10^5$, $2\cdot 10^5$, $5\cdot 10^5$, and $10^7$. Unramified stagnation conjecture. The relative frequency of unramified nilets with $\varrho=0$ decreases from $89.1\%$ through $88.6\%$ and $87.9\%$ to $86.3\%$, while the relative frequency of unramified singlets with $\varrho=1$ increases from $10.9\%$ through $11.4\%$ and $12.1\%$ to $13.6\%$; all singlets have permanent type $\delta_1$. The relative frequency of unramified quartets with $\varrho=2$ is below $0.1\%$, with the listed mixed and pure types occurring in the percentages stated in the source. These computationally observed frequencies are intended as heuristic predictions; the surrounding text notes that some components are proved by the cited theorems, while the asymptotic behavior remains conjectural.